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g(x)=15-4x h(x)=(3)/(2)x+8 Write g(h(x)) as an expression in terms of x. g(h(x))=

g(x)=15−4x g(x)=15-4 x \newlineh(x)=32x+8 h(x)=\frac{3}{2} x+8 \newlineWrite g(h(x)) g(h(x)) as an expression in terms of x x .\newlineg(h(x))= g(h(x))=

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Q. g(x)=15−4x g(x)=15-4 x \newlineh(x)=32x+8 h(x)=\frac{3}{2} x+8 \newlineWrite g(h(x)) g(h(x)) as an expression in terms of x x .\newlineg(h(x))= g(h(x))=
  1. Substitute h(x)h(x) into g(x)g(x): To find g(h(x))g(h(x)), we need to substitute the expression for h(x)h(x) into the function g(x)g(x).
    g(x)=15−4xg(x) = 15 - 4x
    h(x)=(32)x+8h(x) = (\frac{3}{2})x + 8
    Substitute h(x)h(x) into g(x)g(x):
    g(h(x)) = \(15 - 44[(\frac{33}{22})x + 88]
  2. Distribute −4-4 inside the brackets: Now, distribute the −4-4 inside the brackets to both terms in the expression (32)x+8(\frac{3}{2})x + 8.\newlineg(h(x))=15−4[(32)x]−4[8]g(h(x)) = 15 - 4[(\frac{3}{2})x] - 4[8]\newline=15−6x−32= 15 - 6x - 32
  3. Combine constant terms: Combine the constant terms 1515 and −32-32.g(h(x))=15−32−6x=−17−6xg(h(x)) = 15 - 32 - 6x = -17 - 6x

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